Thursday, 13 March 2014

A quantum version of Zeno's paradox

The quantum Zeno effect describes the situation where an unstable particle, say a radioactive atom, won’t decay if it is observed continuously. More generally, it says that if you repeatedly interact with a quantum system through measurement then you can effectively freeze its quantum state.

The phenomenon is named after a Greek philosopher of ancient times, Zeno of Elea. Zeno is known best for a set of paradoxes (we know of 9 of them) that he posed as arguments  against Aristotle’s concept of motion. Here we are interested in the arrow or fletcher’s paradox.

If you observe an arrow flying through the air at some particular instant in time, then it would have a definite position, meaning it isn’t moving at that specific moment. However, you can think of the arrow’s motion as happening one moment at a time. This says that motion must be impossible since it is made up of this long sequence of motionless moments. 

Of course, as far as we can tell, the world is not static and objects in it are not forever motionless. What’s lacking with Zeno’s assertion is the mathematical notion of continuity. Motion is possible because time doesn’t flow like a series of separate frames in a film but more like the seamless current of a steady stream.

Saturday, 8 March 2014

Spins, magnets, and quantum mechanics

Quantum mechanics is often described as an area of physics that deal with energy and matter at the atomic scales, where different weird, unusual stuff happen. To some extent, it is true that quantum objects behave in ways that seem counter to our everyday, common-sense intuition. Unfortunately, focusing on these particular aspects of quantum theory might give the impression that it is mysterious, mystical, and difficult to understand. And that is simply not true. Things like superposition require a little getting used but, for the most part, quantum mechanics works in ways you expect and that naturally make sense. 

I hope to demonstrate this by discussing an experiment with atoms and magnets that is explained in fairly simple terms using quantum mechanics.  This is largely how I was  introduced to the subject many years ago. But to start, we will need to go over some basic ideas regarding magnets and magnetic fields.

Most of us are familiar with magnets from their ability to attract iron and similar metals but in physics, a magnet is just any material that produces a magnetic field. A magnet influences its surroundings through the magnetic field it creates and reacts to the magnetic fields it experiences from other magnetic objects.

A nice thing about magnets is we can understand how they work without having to be very precise. I'm sure many of you have played around with a bar magnet before, which is often found bent into a horseshoe shape, to create a region of particularly strong magnetic field in between the ends labeled north pole and south pole. You probably also know about and maybe experienced first-hand how opposite poles attract and similar ones repel, and how they attract or repel more when two magnets are brought closer together.  
Something less familiar is what determines the force at which a magnet attracts and repels objects. The strength of a magnet is measured by a property called magnetic moment, which is responsible for a magnet's tendency to align with magnetic fields.

Monday, 3 March 2014

Orthogonal states and quantum contextuality

In this post, we use the idea of orthogonal quantum states to describe a fascinating result in quantum mechanics known as the Kochen-Specker theorem. To begin, we review a bit of necessary mathematics.

Recall our usual example of a qubit represented by the spin of an electron. Typically, write the state |E) of such an electron as a superposition of the spin pointing up, which we write as the state |u), and spin pointing down, which we write as the state |d):

|E) = a |u) + b |d),

where a and b are numbers such that |a|^2 is the probability of measuring the spin as up and |b|^2 is the probability of measuring the spin as down.

We've seen before that the set of all possible states for a qubit corresponds to all possible directions the spin can point to, which can be described by using points on a sphere. However, we may choose to write our qubit states using any pair of polar opposite points, and normally we would choose the directions corresponding to north and south pole, which are labeled as the spin states |u) and |d), respectively.

Thursday, 27 February 2014

That remarkable theorem by Bell

Before quantum physics came along, assigning a state to a physical system meant that you can uniquely determine the value of any measurable property using that state. In quantum mechanics, however, we've learned this is not the case: even if you know the quantum state exactly, for most measurements the best you can hope for is to estimate the probabilities for the various possible outcomes.

You might wonder, is the inability to uniquely determine measurement outcomes just a lack of complete knowledge about the system? Or put differently, could you gain some additional information beyond the quantum state that will help you determine outcomes exactly? The answer is "no", quantum phenomena are fundamentally probabilistic in nature and one way to show this is using an argument first made by John Bell in the 1960s.

Bell's theorem, as the result is called, says that there is no hidden mechanism that decides the outcome of a quantum measurement. The way the argument works is that if you assume that there is some  unknown factor that manufactures the statistical results of a measurement, then you can establish a limit on the amount of correlation among certain properties you can measure, which you can state as a Bell inequality. You can then show that there are always some quantum states that can violate the inequality. In this post, we attempt to describe a simple example of Bell's theorem at work.

Monday, 24 February 2014

Understanding quantum entanglement

As mentioned before, a quantum computer exploits the rules of quantum theory for accomplishing feats that are considered impossible with conventional computers. Two features of quantum mechanics are often involved in achieving such feats: superposition, which was discussed in our last post, and entanglement, which is the topic here.

Quantum entanglement is considered to be one of the counterintuitive aspects of quantum mechanics. However it is not a particularly difficult concept to grasp if we start with the notion of correlation. Roughly speaking, entangled quantum systems are objects whose properties so strongly correlated that using a state to describe all of them as a single unit describes them better than assigning a state to individual parts.

Wednesday, 19 February 2014

A note on quantum superposition

Quantum computing is commonly described as the means of harnessing the laws of quantum mechanics to process information, usually for the purpose of doing certain calculations faster than what you can achieve with conventional computers. 

A typical computer operates on binary digits, or bits, of information, which is a sequence of zeros and ones encoded by electrical signals. A calculation is performed using a circuit of transistors designed to switch the signals on and off in a particular way, so that the final bit values determine the result.  The list of specific steps needed for handling bits in any such calculation is called an algorithm.

In contrast,  a quantum computer encodes information in quantum bits, or qubits. Computation with qubits is different from computation with bits because quantum systems can be prepared and controlled in ways that can not be achieved with signals that represent bits. Quantum algorithms describe ways in which qubits can be manipulated so that the correct measurement yields the desired outcome of a calculation with high probability.

Saturday, 1 February 2014

Energy transfer in light-harvesting pigments exhibits non-classical effects

In a previous post, we described the coherent transfer of energy from sunlight in photosynthetic systems. What it shows there is some indication of quantum effects playing a useful role in organic processes. What it does not show is whether there exists a different mechanism for explaining the same effect without using quantum mechanics.

To convince anyone that quantum effects play an important function in biological processes such as photosynthesis, we must show that a classical explanation is not sufficient to account for the efficient transport of energy. In a paper by O'Reilly and Olaya-Castro, they demonstrate this using methods in the quantum theory of light.

Light is a form of electromagnetic radiation, where the term is reserved mainly for radiation that is visible to our eyes. It is composed of electromagnetic waves that vibrate at different frequencies, which we perceive as different shades of colors. Much of how light waves behave can be explained using a classical theory of waves, which describes how waves can be combined to produce various patterns of interference.